Into the Blue: Boldly Going Where Captain Cook Has Gone Before by Tony Horwitz 480pp, Bloomsbury, £20

Why is Captain James Cook so much less celebrated and remembered than Nelson, or even Scott of the Antarctic, after his much more productive and influential voyages and discoveries, from New Zealand and Australia to Alaska and Hawaii? Cook did more than any other 18th-century traveller to change our perceptions of the globe, as he mapped out much of the Pacific and showed that there was no navigable north-west passage to India.

Cook, the son of a Yorkshire farm-labourer, went to sea and showed unusual skills in navigation and leadership. He came to be entrusted by the Admiralty with its most crucial assignments. And he wrote vividly about his experiences in his diaries, with a tolerant humanity and a deep curiosity about the Aborigines, Maoris or Hawaiians - before they eventually killed him. Yet until recently, Cook was only known vaguely as the discoverer of Australia, and associated with the convicts who followed him to Botany Bay. As recently as 1959 his house in Mile End Road, in London, was demolished to make way for a brewery.

Tony Horwitz, a journalist on The New Yorker, set out to rectify this public ignorance and neglect by making his own bold journey. He began following in Cook's footsteps, and recording two stories: Cook's original voyages and his own retracing of them, re-examining what has happened to the territories Cook discovered two centuries earlier.

Horwitz begins with a fine piece of reporting, as he spends a week as an ordinary seaman on board the modern replica of Cook's boat, Resolution. He vividly describes the horrors of climbing the masts to furl the sails, sleeping in a hammock, hauling on the anchor while the ship tosses and surges - thus setting the scene for Cook's far worse conditions two centuries earlier.

And he credibly explains the social background in England that lay behind Cook's first voyage to the Pacific. The privations of the crew appear all the more severe in contrast to the conditions for the one rich sponsor who was accompanying them, with a retinue of servants, in his own relatively luxurious quarters: Joseph Banks, the plant collector who would transform British horticulture. Banks's parallel accounts of the Pacific landfalls add spice to Cook's own diaries. Together the two records provide a unique insight into the psychology and motivation of explorers in the late 18th century, and - more important - into the isolated societies of exotic peoples before they first encountered Europeans.

Cook's diaries are often so eloquent that some readers may long to read his version without interruption. But Horwitz adds an extra dimension by following up each stage of Cook's three great voyages - the first two across the South Pacific, the last to Alaska and Hawaii - describing the subsequent decay and corruption of those societies. And he takes with him a randy and impatient Australian buddy called Roger who supplies suitably bawdy and disrespectful repartee.

The travels of Tony and Roger provide a comic subplot to Cook's adventures; but as Cook's travels become more dramatic, and eventually tragic, the sub-plot seems to be taking over, with digressions that detract from a story that is quite gripping enough in itself. In Hawaii the author finds a monument to the great navigator being sprayed by a Gauguin-esque youth with the words "Capt Crook" and "Whitey Go Home". A woman describes Cook as a "syphilitic racist" and is proud that her people had finally killed him off.

Horwitz himself has interesting reflections about the consequences of Cook's voyages, and he retains and extends his admiration for his hero, despite his lapses into violence and brutality. "If there was an overwhelming message in his journals," he concludes, "it was that people... were alike in their essential nature - even if they ate their enemies, made love in public, worshipped idols, or, like Aborigines, cared not at all for material goods."

And by juxtaposing the heroic ordeals of the 18th-century explorers with the laziness and corruption of later tourists and inhabitants, Horwitz makes Cook appear all the more heroic.